Research on what is now called quantum computing traces back to Richard Feynman, See, e.g., R. Feynman, Int. J. Theor. Phys., 21, 467-488 (1982). Feynman noted that quantum systems are inherently difficult to simulate with classical (i.e., conventional, non-quantum) computers, but that this task could be accomplished by observing the evolution of another quantum system. In particular, modeling the behavior of a quantum system commonly involves solving a differential equation based on the Hamiltonian of the quantum system. Observing the behavior of the quantum system provides information about the solutions to the equation.
The quantum computer is rapidly evolving from a wholly theoretical idea to a physical device that will have a profound impact on the computing of tomorrow. A quantum computer differs principally from a conventional, semiconductor chip-based computer, in that the basic element of storage is a “quantum bit”, or “qubit”. A qubit is a creature of the quantum world: it can exist in a superposition of two states and can thereby hold more information than the binary bit that underpins conventional computing.
Quantum computing generally involves initializing the states of a set of N qubits (quantum bits), creating controlled entanglements among the N qubits, allowing the states of the qubit system to evolve, and reading the qubits afterwards. A qubit can be made from a system having two degenerate quantum states, i.e., states of equal energy, with a non-zero probability of the system being found in either state. Thus, N qubits can define an initial state that is a combination of 2N classical states. This initial state is said to be entangled and will evolve, governed by the interactions which the qubits have both among themselves and with external influences. This evolution defines a calculation, in effect 2N simultaneous classical calculations, performed by the qubit system. Reading out the qubits determines their states and thus the results of the calculations.
Initial efforts in quantum computing concentrated on “software development” or building the formal theory of quantum computing. Software development for quantum computing involves attempting to set up the Hamiltonian of a quantum system that corresponds to a problem requiring solution. Milestones in these efforts were the developments of Shor's algorithm for factoring of a natural number, see P. Shor, SIAM J. of Comput., 26:5, 1484-1509, (1997), and Grover's algorithm for searching unsorted databases, see L. Grover, Proc. 28th STOC, 212-219, (1996). See also A. Kitaev, LANL preprint quant-ph/9511026 (1995).
One proposed application of a quantum computer is the efficient factorization of large numbers, a feat which becomes possible with the Shor algorithm. In applying such a capability, a quantum computer could render obsolete all existing “public-key” encryption schemes. In another application, a quantum computer (or even a smaller scale device such as a quantum repeater) could provide absolutely safe communication channels where a message cannot be intercepted without being destroyed in the process. See, e.g., H. J. Briegel, W. Dur, J. I. Cirac, P. Zoller, LANL preprint quant-ph/9803056 (1998).
One of the principal challenges in quantum computing is to establish an array of controllable qubits, so that large scale computing operations can be carried out. Showing that fault-tolerant quantum computation is theoretically possible opened the way for attempts at practical realizations of quantum computers. See, e.g., E. Knill, R. Laflamme, and W. Zurek, Science, 279, 342, (1998). Several physical systems have been proposed for the qubits in a quantum computer. One system uses molecules that have degenerate nuclear spin states, see N. Gershenfeld and I. Chuang, “Method and Apparatus for Quantum Information Processing”, U.S. Pat. No. 5,917,322. In such a system, nuclear magnetic resonance (NMR) methods can read the spin states. These systems have successfully implemented a search algorithm, see e.g., M. Mosca, R. H. Hansen, and J. A. Jones, “Implementation of a quantum search algorithm on a quantum computer,” Nature, 393:344-346, (1998) and references cited therein, and a number ordering algorithm, see e.g., L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve and I. L. Chuang, “Experimental realization of order-finding with a quantum computer,” Los Alamos National Laboratory preprint quant-ph/0007017, (2000). The number ordering algorithm is related to the quantum Fourier transform, an essential element of both Shor's and Grover's algorithms. However, efforts to expand such systems to a commercially useful number of qubits have faced difficult challenges. One of the principal challenges in quantum computing is to establish an array of controllable qubits, so that large scale computing operations can be carried out.
In 1962, Josephson proposed that non-dissipating current would flow from one superconductor to another through a thin insulating layer, see B. D. Josephson, Phys. Lett., 1:251, (1962). Since then, the so-called Josephson effect has been verified experimentally and has spawned a number of important applications of superconducting materials.
One physical implementation of a phase qubit involves a micrometer-sized superconducting loop with 3 or 4 Josephson junctions. See J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, “Josephson Persistent-Current Qubit”, Science, 285:1036-1039, (1999), which is incorporated herein by reference in its entirety. The energy levels (or basis states) of this system correspond to differing amounts of magnetic flux that thread the superconducting loop. Application of a static magnetic field perpendicular to the plane of the loop may bring two of these levels into degeneracy. Typically, external alternating current electromagnetic fields are applied to enable tunneling between non-degenerate states. Thus, the Josephson persistent-current qubit provides a mechanism for tuning the qubit basis states so that they become degenerate and thereby allow quantum interaction between the two states. In practice, this is achieved by inductively coupling a second superconducting loop to the loop that acts as a qubit, and by modulating the supercurrent through the second loop. However, it has been found that this inductive coupling limits the usefulness of the device, and a method for providing degenerate basis states that does not require interaction with the qubit would be ideal.
To address this problem, a ground state π-phase shifter (π-junction) can be included in a superconducting loop. See, e.g., G. Blatter, V. Geshkenbein, and L. Ioffe, “Design aspects of superconducting-phase quantum bits”, Phys. Rev. B, 63, 174511, (2001) and references cited therein. Blatter et al., illustrate how to make use of π-junctions in a superconducting loop to shift the ground state phase by ±π/2. Blatter et al., describe a π-junction using a superconductor-ferromagnet-superconductor junction structure, but teach away from the use of unconventional d-wave superconductors, because they are regarded to be nontrivial to fabricate.
Another implementation of a phase qubit is a permanent readout superconducting qubit (PRSQ), first disclosed by A. Zagoskin in commonly-assigned U.S. patent application Ser. No. 09/452,749, “Permanent Readout Superconducting Qubit”, filed Dec. 1, 1999, incorporated herein by reference in its entirety. The PRSQ includes two regions of unconventional superconducting material, separated by a Josephson junction such as a grain boundary, and further having a crystal lattice mismatch. A first of the two superconducting regions is large, so that the phase of the superconductor is fixed, and a second of the two regions is mesoscopic in size. The second superconducting region forms a qubit having the basis states ±φ0, where φ0 is a quantum of phase with respect to the phase φB of the large superconducting region.
Two types of superconductors are regularly used nowadays: conventional superconductors and unconventional superconductors. The most important phenomenological difference between the unconventional superconductors and conventional superconductors is in the orbital symmetry of the superconducting order parameter. In the unconventional superconductors, the pair potential changes sign depending on the direction of motion in momentum space. This has now been experimentally confirmed; see e.g., C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys., 72, 969, (2000).
A system has recently been proposed wherein a network of grain boundaries links a group of polygon-shaped crystal superconductors. See, e.g., C. Tsuei, and J. Kirtley, “Pairing symmetry in cuprate superconductors”, Rev. Mod. Phys., 72, 969 (2000). The structure can be formed using a technique described in C. Tsuei, J. Kirtley, C. Chi, L. Yu-Jahnes, A. Gupta, T. Shaw, J. Sun, and M. Ketchen, “Pairing Symmetry and Flux Quantization in a Tricrystal Superconducting Ring of YBa2Cu3O7−δ”, Phys. Rev. Lett., 73, 593 (1994). The superconducting materials can violate time reversal symmetry and it can be shown that flux can be trapped and maintained in the region where three of the crystals meet. Each of the crystals has an objective crystal lattice alignment, and the network can in principle be unlimited in size. The trapped flux can be used as a qubit in quantum computing, although the usefulness of the structure is limited since it is difficult to efficiently interact with, and provide control of, the intersection points to measure the flux without disrupting the entire structure. A mechanism that would allow for control and interaction of such a system would be extremely useful.
In general, then, given the potential of quantum computing, there is a need for robust and commercially scalable qubit designs.